The only public showers are at "Freshen Up" the international terminal. From the SFO website :

Shower facilities are available at Freshen Up! located on the
Departures/Ticketing Level of the International Terminal, near the
entrance to Gates G91-G102. Freshen Up! is open daily from 7:00 a.m.
to 11:00 p.m. For additional information call 650.877.0798.